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Two identical rectangular blocks can be arranged either in configuration I or configuration II as shown. One block has thermal conductivity k and the other 2k. The temperature difference across the ends along the x-axis is the same in both configurations. If it takes 9 s to transport a certain amount of heat from the hot end to the cold end in configuration I, the time to transport the same amount of heat in configuration II is:

1. 2.0 s
2. 3.0 s
3. 4.5 s
4. 6.0 s

Correct answer: 2.0 s

Solution

The series arrangement (config I) carries a smaller heat current than the parallel arrangement (config II); the heat current ratio H_II/H_I = 9/2, so the time drops from 9 s to 9*(2/9) = 2.0 s.

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